(1)	$\begin{array}{l}\displaystyle q_W = a \cdot q_O + b\end{array}$

where

(2)	$\begin{array}{l}\displaystyle a = J^{-1}_O \cdot ( J_{1W} + J_{2W})\end{array}$

(3)	$\begin{array}{l}\displaystyle b = J_{2W} \cdot (p^_2 - p^_1)\end{array}$

In practical applications, the equation (1) is often considered through the averaged value:

(4)	$\begin{array}{l}\displaystyle < q_W> = a \cdot < q_O> + b\end{array}$

where

$\begin{array}{l}< q_W>, \ < q_O>\end{array}$

are weighted average of $\begin{array}{l}q_W\end{array}$ and $\begin{array}{l}q_O\end{array}$

There are different ways to calculated weighted average of the dynamic variable, for example:

t-weighted

q-weighted

$\begin{array}{l}\displaystyle \bigl A \bigr = \frac{1}{t} \int_o^t A(t) \, dt\end{array}$

$\begin{array}{l}\displaystyle < A>_q = \frac{1}{Q(t)} \int_o^t A(t) \, q(t) \, dt\end{array}$

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See Also